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Note 5, p. 12. As those of number are not those of plane surfaces, &c.] That is, the science of number differs, generically, from that of Geometry. The nature, so to say, of numbers had been a subject of deep and curious speculation long before and during the age of Aristotle, and there lie scattered through his works notices of writers and systems which, although in themselves interesting to scholars, would, even were it possible to give a clear summary of them, be foreign to the present inquiry. Aristotle[1], before entering upon number, defined "quantity" as being, partly definite, and partly continuous—and the former he constituted of parts which have no mutual local relation to each other; the latter of parts which have that relation. The "definite" quantity is represented "by number and by a word; the continuous by line, surface, solid, and time and place, besides." In order to shew that number is definite or discontinuous, he observes, "there is no common boundary whereon the parts of any number conjoin; as if, for instance, five or three be parts of ten, there is no common boundary whereon five or seven can conjoin to make the whole number, but each part is, for ever, a distinct number, and thus number is among definite quantities." "Words are, in like manner, among definite quantities; and it is manifest that words, uttered by the voice, are quantity, in that they are measurable by long and short syllables, and manifest too that there is no common boundary